Abstract: A class of Marcus contextual languages containing non-context-free languages is defined. A parser for this class of languages is developed. The parser uses an operatorial automaton and it works in square time in the length of the input words.

Abstract: We introduce and study relations on words which generalize the factor relation, being restrictions of the subword relation. We give an equivalent condition for the finite basis property for these relations which generalizes the well-known theorem of Higman. Some language-theoretic gaps for infinite antichains are also presented.

Abstract: We consider operations between languages, based on splitting the underlying alphabet into two disjoint sets, one of them having some priority. Such operations are generalizations of the classical catenation or shuffle operation, with which rational, linear and algebraic languages can be defined similar to the classical case. The basic properties of the corresponding language families are investigated too.

Abstract: The grammatical inference problem is solved for a class of languages which can be generated by pure grammars with non-shortening productions. Necessary and sufficient condition for determination whether a language belongs to this class is formulated and proved. Finally, an algorithm for assigning a pure grammar to any language from the class is described.

Abstract: Two strategies of parallel adjoining of contexts are considered for contextual grammars with choice. After a short comparison between them, there are provided Chomsky-Schutzenberger type characterizations of context-free and recursively enumerable languages. Finally, we discuss some decision problems.

Abstract: In [13] pure generalized grammars were studied, in particular, the problem of reducing a pure generalized grammar to a pure grammar. These results are transferred to the so called pregrammars in the present paper. The obtained results may be applied not only to pure generalized grammars but also to other structures.